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arXiv:2102.01032 · Physical Review A

Superposition of two-mode squeezed states for quantum information processing and quantum sensing

Fernando Redivo Cardoso, Daniel Z. Rossatto, Gabriel P. L. M. Fernandes, Gerard T. Higgins, Celso J. Villas-Bôas

Published Jun 2, 2021• 48 citations
arXivHTMLPDF

Abstract

We investigate superpositions of two-mode squeezed states (TMSSs), which have potential applications in quantum information processing and quantum sensing. We study some properties of these nonclassical states such as the statistics of each mode and the degree of entanglement between the two modes, which can be higher than that of a TMSS with the same degree of squeezing. The states we consider can be prepared by inducing two-mode Jaynes-Cummings and anti-Jaynes-Cummings interactions in a system of two modes and a spin-$\frac{1}{2}$ particle, for instance, in the trapped ion domain, as described here. We show that when two harmonic oscillators are prepared in a superposition of two TMSSs, each reduced single-mode state can be advantageously employed to sense arbitrary displacements of the mode in phase space. The Wigner function of this reduced state exhibits a symmetrical peak centered at the phase-space origin, which has the convenient peculiarity of getting narrower in both quadratures simultaneously as the average photon number increases. This narrow peak can be used as the pointer of our quantum sensor, with its position in phase space indicating the displacement undergone by the oscillator.

DOI
10.1103/physreva.103.062405

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We investigate superpositions of two-mode squeezed states (TMSSs), which have potential applications in quantum information processing and quantum sensing. We study some properties of these nonclassical states such as the statistics of each mode and the degree of entanglement between the two modes, which can be higher than that of a TMSS with the same degree of squeezing. The states we consider can be prepared by inducing two-mode Jaynes-Cummings and anti-Jaynes-Cummings interactions in a system of two modes and a spin-12\frac{1}{2}21​ particle, for instance, in the trapped ion domain, as described here. We show that when two harmonic oscillators are prepared in a superposition of two TMSSs, each reduced single-mode state can be advantageously employed to sense arbitrary displacements of the mode in phase space. The Wigner function of this reduced state exhibits a symmetrical peak centered at the phase-space origin, which has the convenient peculiarity of getting narrower in both quadratures simultaneously as the average photon number increases. This narrow peak can be used as the pointer of our quantum sensor, with its position in phase space indicating the displacement undergone by the oscillator.
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.
Abstract Recently, photon subtraction from the single-mode squeezed vacuum state (SVS) has been explored as a technique to enhance its squeezing strength (SS). Notably, the enhancement is observed only when an even number of photons is subtracted, and this effect is limited to a specific range of the squeezing parameter r. In this paper, we introduce a novel class of single-mode nonclassical states, termed as qubit superposed SVSs (qSSVSs), via the coherent superposition of a SVS and a single-photon-subtracted SVS. The primary objective of this work is to enhance the SS for any r > 0 through the creation of these superposed states. Our analysis reveals that the qSSVSs not only improve the SS but also exhibit enhanced nonclassical features such as the negativity of Wigner function, single-mode antibunching effect, photon-number distribution, and sub-Poissonian photon statistics. Furthermore, we demonstrate that the qSSVSs provide superior phase sensitivity in a quantum Mach–Zehnder interferometer compared to the original SVS. Importantly, the generation of qSSVSs is feasible using readily available optical devices, including a beam splitter, a photodetector, and an amplitude displacement. These states hold significant potential for practical applications in quantum information science, particularly for tasks such as information encoding and processing in quantum computing systems.
Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.
We show that superpositions of oppositely squeezed states -- non-Gaussian Schr{ö}dinger-cat-like states -- exhibit enhanced nonclassical features and provide an entanglement advantage in the small-squeezing regime. These states possess photon-number structures distinct from conventional coherent-state cat states, and we analyze their Wigner functions and the entanglement generated when they are injected into a 50-50 beam splitter. As a practical application, we demonstrate that they enable a high-quality heralded single-photon source whose second-order intensity correlation function is smaller than that obtained from a pure two-mode squeezed vacuum state. We further propose a linear-optical heralding scheme that approximates these superpositions without requiring strong Kerr nonlinearities. Our results indicate that the superposition of oppositely squeezed states is a promising non-Gaussian resource for quantum information processing, particularly for single-photon generation.
We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states—hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are , i.e., their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of 8.7 dB of spin-dependent squeezing 15 times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.